Active control of polarization states of electromagnetic waves is important in applications of information processing, telecommunications, and spectroscopy. However, despite the recent advances using artificial materials [1,2], most active polarization control schemes require optical stimuli requiring complex optical setups. Recently, we experimentally demonstrated that the polarization state of terahertz waves can be tuned electrically [3]. Combining a chiral metamaterial with a gated single-layer sheet of graphene, we showed that transmission of a terahertz wave with one circular polarization can be electrically controlled without affecting that of the other circular polarization, achieving large intensity modulation depths (>99%) with a low gate voltage. This effective control of polarization is made possible by the full accessibility of three coupling regimes, that is, underdamped, critically damped, and overdamped regimes by electrical control of the graphene properties.

In this work, to quantitatively understand the control of coupling, we derive an analytical expression of transmission coefficients by taking account of the two resonances in the graphene chiral metamaterial and investigate how damping coefficients play a role in varying the coupling regimes. In particular, we employed the coupled mode theory to derive the transmission coefficients [4]. Because there are three coupling channels between the incident and transmitted waves, that is, two via the resonance modes and one direct coupling, the complex transmission amplitude coefficient for right-handed circular polarization can be written as a sum of two Lorentzian functions and one constant transmission. The analytical expression provides us with a clear explanation on how to access critical coupling by changing the gate voltage in graphene chiral metamaterials.